带大初值的有界区间内可压缩Navier-Stokes-Korteweg系统的毛细极限消失问题
Vanishing capillary limit for compressible Navier-Stokes-Korteweg system in a bounded interval with large initial data
AI总结：
本文针对有界区间内带大初值的等熵可压缩Navier-Stokes-Korteweg系统，推导一致耗散估计与校正项，得到解的最优收敛速率，严格推导出等熵可压缩Navier-Stokes系统。
AI中文摘要：
本文研究有界区间内等熵可压缩Navier-Stokes-Korteweg系统的毛细极限消失问题，主要挑战在于毛细项与边界效应。研究推导了关于密度三阶导数的新型一致耗散估计及若干校正项以应对这些困难，这使得在任意大初值下，解的L^∞范数能得到全局时间的最优收敛速率。本工作通过毛细极限消失，严格推导了有界区间内等熵可压缩Navier-Stokes系统，该系统源自等熵可压缩Navier-Stokes-Korteweg系统。
英文摘要：
In this paper, we study vanishing capillary limit for isentropic compressible Navier-Stokes-Korteweg system in a bounded interval. The main challenges focus on the capillary term and the boundary effect. A new uniform dissipative estimate in terms of the third-order derivative of density and some correctors are derived to handle such difficulties. It leads to the optimal convergence rate of the solutions in $L^\infty$ norm globally in time with arbitrarily large initial data. This work provides a rigorous derivation of the isentropic compressible Navier-Stokes system in a bounded interval from the isentropic compressible Navier-Stokes-Korteweg system via vanishing capillary limit.
